Armstrong said the child was calmly sitting in her seat, but Southwest employees still decided to have the family kicked off the flight.
Her video, which has been viewed more than 500,000 times on Facebook, shows the father talking to a male attendant about how he was 'trying to calm' his baby.
He also tells the man that a female flight attendant had been "yelling at my baby".
The man then tells the father, who was also traveling with another woman, that they need to grab their bags and leave.
"But she's sitting," the father replies. "I don't understand."
"You're gonna leave," the Southwest employee tells him as the flight attendant, who Armstrong said was named Michelle, returns.
"But she's sitting," the father says again. 'She's been sitting for the last five minutes.'
"I explained the FAA regulations," Michelle replies. "There's no more discussion, we're back at the gate."
Michelle then claims that the father told her to "get out of' his daughter's face, a claim that Armstrong disputed on the spot.
"No, I think he asked you if he could have a minute to calm her down,' she tells Michelle. "Not for you to get out of her face."
"He asked for a minute,' another fellow passenger chimed in.
Michelle then turns to the women trying to defend the father and says, "We're cleared for departure, you all need to understand the operation."
"She's a child, she was scared, Armstrong responds.
"This is not helpful guys, you want to go to Atlanta? The decision has been made," Michelle retorts.
"So you're going to kick them off the flight and traumatize her some more, to have her fearful to get on the plane again when she's calm?" Armstrong asks.
At this point someone turns to Armstrong and says, 'This has nothing to do with you, so why don't you stop filming.'
"No, I'm going to keep filming," she tells them.
She then turns her camera back to the family, where the male flight attendant is telling the father, 'We're just trying to keep this as simple as possible, you cannot fly on this flight.'
The little girl then begins to whimper as her father, who has not been identified, takes her in his arms.
"I'm glad you screwed up everyone's day," he tells Michelle before exiting the plane.
Armstrong posted the video on Facebook after the flight, writing 'shame on you Southwest' in the caption.
"Southwest Airlines kicked a man off the plane with his two-year-old daughter because she was afraid and not sitting in her own seat," she wrote.
"He asked the lady for a minute to calm her down, she walked away and called people to remove him."
"The baby was already calm by now and sitting in her own seat. Captain then came over the intercom to say we will be going back to the gate to handle a customer service issue."
"They then told me to stop filming and that this issue did not involve me, and that me and another woman who spoke up will be the next off the plane".
Armstrong, of Joliet, said she filmed the video because she wanted the company to see it and apologize to the family.
"I am a mom and my heart was hurting for this dad," she told WGN. "Southwest owes them an apology."
"I did not think this would blow up," she added. "I am not sure why I even began to film. I just knew from the woman's attitude and security approaching it wasn't going to end well."
Southwest told DailyMail.com that a "conversation escalated on board between the crew and a customer traveling with a small child".
"We always aim for a welcoming and hospitable experience and regret the inconvenience to all involved," it continued.
"The traveling party was booked on then next flight to Atlanta after the original flight continued as planned."
"We will reach out to the customer(s) to listen to any concerns they have about their experience and look forward to welcoming them on board soon."
